4 pagesInternational audienceThe name of Etienne Bézout is well-known in mathematics, but we are only now able to throw some light on his mathematical carreer and his exact achievements. Bézout (1730-1783) was recruited at the Paris Academy of Sciences in 1758, after two papers on Dynamics and Integral calculus. He began working on algebraic analysis in 1762, presenting in particular on February 1st, 1764, an important work on elimination. However, a few months later, he was appointed examiner for the Navy's officers schools and put in charge of reforming mathematical studies in these schools; the Artillery School was added to his load in 1768. With most of his time on the road, visiting six officers' schools all around France, he restricted his research interest to one topic only, Algebraic Analysis, essentially the theory of equations; however, he also wrote mathematical textbooks which remain best-sellers for about a century. The closure of the artillery schools in 1773, by order of the king, allowed Bézout to turn again to more advanced projects, in particular his most famous work, the General Theory of Algebraic equations published in 1779; it contains one of his most famous result, the theorem which bears his name in actual algebraic geometry. Here, we will briefly explain how he reduced elimination for systems of n equations with n unknowns to the establishment of conditions for the existence of solutions to linear systems; study his specific use of indeterminate coefficients to find the degree of the resultant and follow him from his algebra textbook to his synthetic treatise on algebraic equations
